Question

How do you factor `12x^2+x-6`?

Answer 1

(3x - 2)(4x + 3)

Explanation:

Use the new systematic AC Method (Socratic Search).
`f(x) = 12x^2 + x - 6 =` 12(x + p)(x + q)
Converted trinomial`f'(x) = x^2 + x - 72 =` (x + p')(x + q').
Find p' and q' that have opposite signs because ac < 0
Factor pairs of (ac = -72) -->... (-6, 12)(-8, 9). This sum is (1 = b).
Then p' = -8 and q' = 9.
Back to f(x) --> `p = (p')/a = -8/12 = - 2/3`, and `q = (q')/a = 9/12 = 3/4`.
Factored form: `f(x) = 12(x - 2/3)(x + 3/4) = (3x - 2)(4x + 3)`